From: Mary Lou (for Teacher2Teacher Service)
Date: May 10, 1998 at 16:23:12
Subject: Re: Use of rational roots

Hi,

The rational roots theorem does not have any applications of which I am
aware. Prior to the use of graphics technology it was necessary to use this
theorem in order to get some idea of the graph of the function. If you could
find the rational roots, locate them on the x-axis, and find the sign value
of the function within the boundaries of the roots, you had a pretty good
idea of what the function looked like. Since most polynomials do not have
solely rational roots, this theorem has limited use.

About twelve years ago, I would give students a fourth degree polynomial and
ask them to sketch a graph. Such a questions could occupy some students for
20-30 minutes. Today, there is no reason for students to spend this much time
when a calculator or computer does it almost instantly.

Spend your time trying to find the irrational roots whenever possible or
start thinking about finding the complex roots for a polynomial such as x^4 +
1 = 0. This has no rational roots since it has no real roots. However, x^3 +
1 = 0 does have at least one real root, which is rational. The other two are
complex.

-Mary Lou

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